A new generalization of the Waring distribution

A tetraparametric univariate distribution generated by the Gaussian hypergeometric function that includes the Waring and the generalized Waring distributions as particular cases is presented. This distribution is expressed as a generalized beta type I mixture of a negative binomial distribution, in such a way that the variance of the tetraparametric model can be split into three components: randomness, proneness and liability. These results are extensions of known analogous properties of the generalized Waring distribution. Two applications in the fields of sport and economy are included in order to illustrate the utility of the new distribution compared with the generalized Waring distribution.